Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups

Wee Teck Gan, Benedict H. Gross, Dipendra Prasad

Published 2009-09-16Version 1

We consider several questions about restriction of representations of classical and metaplectic groups over local and global fields to subgroups, extending considerably the scope of the earlier work on $SO(n),SO(n-1)$. This includes Bessel and Fourier-Jacobi models too. We formulate several conjectures about these restriction problems involving root numbers of symplectic representations in the local case, and central critical L-value in the global case. Along the way we prove several results both in number theory and representation theory.